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A223987 T(n,k)=Number of nXk 0..3 arrays with rows unimodal and columns nondecreasing.

%I A223987 #6 Jul 23 2025 04:46:14
%S A223987 4,16,10,50,100,20,130,684,400,35,296,3526,5029,1225,56,610,14751,
%T A223987 44803,25410,3136,84,1163,52591,308470,358118,99634,7056,120,2083,
%U A223987 165212,1738756,3770722,2086196,325120,14400,165,3544,468292,8350154,31585056
%N A223987 T(n,k)=Number of nXk 0..3 arrays with rows unimodal and columns nondecreasing.
%C A223987 Table starts
%C A223987 ...4....16.......50........130.........296...........610...........1163
%C A223987 ..10...100......684.......3526.......14751.........52591.........165212
%C A223987 ..20...400.....5029......44803......308470.......1738756........8350154
%C A223987 ..35..1225....25410.....358118.....3770722......31585056......219861244
%C A223987 ..56..3136....99634....2086196....31831914.....378122264.....3661410444
%C A223987 ..84..7056...325120....9647292...204647416....3322756326....43307637038
%C A223987 .120.14400...922768...37395816..1067023886...22985966340...392525216516
%C A223987 .165.27225..2346883..126087157..4710529013..131366850521..2873859236297
%C A223987 .220.48400..5462600..379654704.18159308422..642224541548.17659521902693
%C A223987 .286.81796.11818092.1040942916.62548820489.2756467192963.93729371629362
%H A223987 R. H. Hardin, <a href="/A223987/b223987.txt">Table of n, a(n) for n = 1..420</a>
%F A223987 Empirical: columns k=1..7 are polynomials of degree 3*k
%F A223987 Empirical: rows n=1..7 are polynomials of degree 6*n
%e A223987 Some solutions for n=3 k=4
%e A223987 ..0..2..1..1....0..0..2..0....0..1..1..0....1..2..0..0....2..2..2..0
%e A223987 ..0..2..2..1....1..1..2..0....0..3..2..1....1..2..2..0....3..2..2..1
%e A223987 ..1..3..3..3....2..3..2..1....3..3..2..1....2..3..3..2....3..2..2..1
%Y A223987 Column 1 is A000292(n+1)
%Y A223987 Column 2 is A001249
%Y A223987 Row 1 is A223659
%Y A223987 Row 2 is A223865
%K A223987 nonn,tabl
%O A223987 1,1
%A A223987 _R. H. Hardin_ Mar 30 2013